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Theory and Simulation

The group 'Theory and Simulation' develops constitutive models for advanced materials such as high strength steels. As the mechanical properties are of main interest crystal plasticity modelling [1] builds the core of the activities. For this purpose a number of constitutive models have been developed in the last 15 years. These models cover the full range from phenomenological descriptions to physics based formulations of dislocation slip and other deformation mechanisms such as twinning induced plasticity (TWIP) and displacive transformations (TRIP). To facilitate the implementation of the models the Düsseldorf Advanced MAterial Simulation Kit (DAMASK, [2]) has been developed.

DAMASK started out as material subroutine for commercial Finite Element Software. Later it was complemented by a so called spectral solver, which serves as a fast alternative to the FEM for the simulation of Representative Volume Elements (RVEs). Currently DAMASK is extended to a multi-field solver to take into account multi-physics problems, e.g. thermal effects or damage. DAMASK is distributed as freeware according to GPL3 and can be downloaded from damask.mpie.de, where you also find a lot more detailed information.

As mentioned before the main scientific focus of the group is the development of advanced constitutive models. One such model is an analytical model for TWIP steels [3] that was developed in the framework of SFB 761 'steel ab initio'. This model is an extension of the 3 internal variable model developed earlier by Roters [4] and its key feature is a physical description for twin nucleation and growth. It is build on the twin model of Mahajan and Chin [5] and uses the stacking fault energy as an important input parameter, which can be derived from ab initio calculations. A modified version of this model has been implemented in the framework of crystal plasticity, i.e. is part of DAMASK, and was recently extended to also account for the TRIP effect [6].

A second constitutive model incorporates the dislocation flux into the state evolution equations. The model distinguishes positive and negative edge and screw dislocations. In case of heterogeneous deformation the then unbalanced dislocation fluxes automatically lead to the creation of so called geometrically necessary dislocations, i.e. an unbalanced number of positive and negative dislocations of one kind. In this way the additional hardening due to deformation gradients is taken into account. The model has very successfully been applied to simulate a wedge indentation experiment [7].


  1. F. Roters, P. Eisenlohr, L. Hantcherli, D. D. Tjahjanto, T. R. Bieler, D. Raabe: Overview of constitutive laws, kinematics, homogenization and multiscale methods in crystal plasticity Finite-element modeling: Theory, experiments, applications, Acta Materialia 58 (2010) 1152 – 1211
  2. F. Roters, M. Diehl, P. Shanthraj, P. Eisenlohr, C. Reuber, S. L. Wong, T. Maiti, A. Ebrahimi, T. Hochrainer, H.-O. Fabritius, S. Nikolov, M. Friák, N. Fujita, N. Grilli, K. G. F. Janssens, N. Jia, P. J. J. Kok, D. Ma, F. Meier, E. Werner, M. Stricker, D. Weygand, D. Raabe: DAMASK – The Düsseldorf Advanced Material Simulation Kit for modeling multi-physics crystal plasticity, thermal, and damage phenomena from the single crystal up to the component scale, Computational Materials Science 158 (2019), 420 – 478
  3. D. R. Steinmetz, T. Jäpel, B. Wietbrock, P. Eisenlohr, I. Gutierrez-Urrutia, A. Saeed-Akbari, T. Hickel, F. Roters, D. Raabe: Revealing the strain-hardening behavior of twinning-induced plasticity steels: Theory, simulations, experiments, Acta Materialia 61 (2013) 494 – 510
  4. F. Roters, D. Raabe, G. Gottstein: Work hardening in heterogeneous alloys - a microstructural approach based on three internal state variables, Acta Materialia 48 (2000) 4181 – 4189
  5. S. Mahajan, G. Y. Chin: Formation of deformation twins in fcc crystals, Acta Metallurgica, 21 (1973) 1353 – 1363
  6. S. L. Wong, M. Madivala, U. Prahl, F. Roters, D. Raabe: A crystal plasticity model for twinning- and transformation-induced plasticity, Acta Materialia 118 (2016) 140 – 151
  7. C. Reuber, P. Eisenlohr, F. Roters, D. Raabe: Dislocation density distribution around an indent in single-crystalline nickel: Comparing nonlocal crystal plasticity Finite-element predictions with experiments, Acta Materialia 71 (2014) 333 – 348
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